How to distribute overlapping objects?
The Distribute operator from the OscurArt Tools addon works fine, however it expects one object from those to be distributed put at the end of the distribution area. This means one should select one object of those overlapping ones, move it away as desired, then select all the others, make the standalone one as active and run Distribute.

There are 5 monkeys overlapping in one spot in the first frame on the image below; one is moved to the right on the second, and then the rest of them are distributed with addon.